MAYBE Termination Proof

Termination Proof

by ttt2 (version ttt2 1.15)

Input

The rewrite relation of the following TRS is considered.

B(x0) → W(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(V(x0))))))))))))))))))))))))
M(x0) → x0
M(V(0(x0))) → V(X0(x0))
M(V(1(x0))) → V(X1(x0))
M(V(2(x0))) → V(X2(x0))
X0(0(x0)) → 0(X0(x0))
X0(1(x0)) → 1(X0(x0))
X0(2(x0)) → 2(X0(x0))
X1(0(x0)) → 0(X1(x0))
X1(1(x0)) → 1(X1(x0))
X1(2(x0)) → 2(X1(x0))
X2(0(x0)) → 0(X2(x0))
X2(1(x0)) → 1(X2(x0))
X2(2(x0)) → 2(X2(x0))
X0(E(x0)) → 0(E(x0))
X1(E(x0)) → 1(E(x0))
X2(E(x0)) → 2(E(x0))
W(V(x0)) → R(L(x0))
L(0(x0)) → Y0(L(x0))
L(1(x0)) → Y1(L(x0))
L(2(x0)) → Y2(L(x0))
L(0(0(0(0(0(1(0(1(2(0(1(1(0(0(0(0(2(0(1(2(2(1(0(x0)))))))))))))))))))))))) → D(2(1(2(0(0(2(2(1(0(1(0(0(1(0(0(0(1(0(2(1(1(2(1(2(2(1(0(x0))))))))))))))))))))))))))))
L(0(0(0(2(1(0(2(1(0(1(1(2(1(2(2(0(0(2(2(1(1(1(0(x0)))))))))))))))))))))))) → D(0(1(0(0(1(0(1(1(2(1(1(1(2(0(0(0(2(1(2(0(0(1(2(1(1(0(1(x0))))))))))))))))))))))))))))
L(0(0(0(2(1(1(0(1(0(1(1(2(2(0(0(2(1(0(2(1(1(1(0(x0)))))))))))))))))))))))) → D(1(0(1(1(2(0(2(1(0(0(0(1(1(0(2(1(0(0(1(0(0(0(1(1(2(1(1(x0))))))))))))))))))))))))))))
L(0(0(0(2(2(1(1(0(1(0(0(2(1(2(0(1(2(1(2(1(0(2(2(x0)))))))))))))))))))))))) → D(1(0(0(0(0(1(0(1(1(1(1(1(0(2(1(0(2(1(2(1(1(0(1(1(0(2(1(x0))))))))))))))))))))))))))))
L(0(0(1(1(0(1(0(0(1(0(0(2(0(1(2(2(0(2(0(1(1(0(0(x0)))))))))))))))))))))))) → D(0(1(2(1(1(2(1(2(2(0(0(2(1(0(0(1(0(1(2(0(2(2(1(1(1(1(0(x0))))))))))))))))))))))))))))
L(0(0(1(2(1(2(2(0(0(0(1(0(0(0(0(1(0(1(2(1(2(0(1(x0)))))))))))))))))))))))) → D(1(0(0(2(0(0(2(1(1(1(0(0(0(0(0(1(0(2(1(1(2(2(1(1(0(1(0(x0))))))))))))))))))))))))))))
L(0(0(2(0(2(1(0(0(2(1(0(1(2(2(2(1(0(1(0(2(1(2(1(x0)))))))))))))))))))))))) → D(1(1(0(0(0(0(1(1(2(0(1(0(2(1(2(2(1(0(0(2(1(0(0(2(1(1(1(x0))))))))))))))))))))))))))))
L(0(0(2(1(1(2(1(0(2(2(2(0(0(0(0(2(2(1(0(1(0(0(0(x0)))))))))))))))))))))))) → D(1(0(2(1(0(1(0(2(1(2(1(1(0(0(2(0(1(0(2(2(1(2(0(1(1(1(0(x0))))))))))))))))))))))))))))
L(0(1(0(2(1(0(2(1(0(1(2(1(0(2(2(2(1(0(0(1(1(2(0(x0)))))))))))))))))))))))) → D(1(0(2(1(1(0(1(0(1(0(0(0(2(0(1(0(2(0(1(0(2(1(1(0(1(1(1(x0))))))))))))))))))))))))))))
L(0(1(0(2(2(1(0(1(2(2(1(0(2(1(1(2(1(2(2(1(2(1(1(x0)))))))))))))))))))))))) → D(0(2(1(0(0(1(2(0(2(2(1(0(2(1(1(1(1(0(1(1(0(0(1(0(0(2(0(x0))))))))))))))))))))))))))))
L(0(1(2(0(2(0(2(2(1(1(0(0(2(1(1(2(0(0(0(0(2(1(1(x0)))))))))))))))))))))))) → D(0(0(0(2(1(1(1(2(0(2(2(2(1(1(0(1(2(1(2(1(0(0(2(0(1(0(1(x0))))))))))))))))))))))))))))
L(0(1(2(1(0(1(1(0(2(0(1(1(2(2(2(1(0(2(2(0(0(1(0(x0)))))))))))))))))))))))) → D(2(1(1(0(1(1(0(2(0(1(2(1(0(1(1(2(2(1(2(2(1(0(0(1(2(0(1(x0))))))))))))))))))))))))))))
L(0(1(2(1(2(1(0(0(1(0(2(0(2(1(1(2(1(1(0(2(1(1(0(x0)))))))))))))))))))))))) → D(0(1(1(1(1(1(1(1(0(1(1(1(2(1(1(0(2(1(2(1(2(1(1(0(0(1(1(x0))))))))))))))))))))))))))))
L(0(1(2(2(2(1(1(2(2(2(2(2(1(0(1(1(1(1(2(1(0(1(1(x0)))))))))))))))))))))))) → D(2(1(2(0(0(1(2(2(1(1(2(0(1(1(0(0(2(2(0(2(1(1(1(0(0(1(1(x0))))))))))))))))))))))))))))
L(0(2(1(0(0(2(0(0(1(1(1(0(1(1(2(1(1(0(1(1(2(1(1(x0)))))))))))))))))))))))) → D(2(1(0(0(1(0(2(1(1(1(1(1(1(1(1(0(2(1(1(0(1(0(0(0(1(2(1(x0))))))))))))))))))))))))))))
L(0(2(2(0(2(1(0(2(0(2(2(1(0(1(0(1(0(0(2(1(0(0(0(x0)))))))))))))))))))))))) → D(0(1(1(2(1(0(1(0(1(1(0(0(1(2(1(1(2(2(1(2(0(1(0(0(1(2(0(x0))))))))))))))))))))))))))))
L(0(2(2(1(0(1(1(0(1(0(2(1(1(0(0(0(0(2(1(0(2(2(2(x0)))))))))))))))))))))))) → D(0(0(0(1(2(1(2(1(1(2(2(2(1(1(0(1(0(2(1(1(0(0(1(2(1(1(0(x0))))))))))))))))))))))))))))
L(1(0(0(0(0(0(0(1(2(1(1(0(2(0(1(2(2(2(2(1(1(0(0(x0)))))))))))))))))))))))) → D(1(2(0(0(2(1(2(1(0(1(1(2(1(0(1(2(1(0(2(1(1(2(1(2(2(2(1(x0))))))))))))))))))))))))))))
L(1(0(0(2(1(1(0(2(1(1(2(0(0(0(2(0(0(0(1(1(1(2(0(x0)))))))))))))))))))))))) → D(1(0(1(0(1(0(2(1(1(1(2(1(0(0(1(0(2(1(0(1(0(2(1(2(2(2(0(x0))))))))))))))))))))))))))))
L(1(0(1(2(0(0(0(2(1(0(0(1(0(0(1(2(2(1(0(2(0(0(0(x0)))))))))))))))))))))))) → D(1(0(0(1(0(2(1(2(2(0(1(0(0(1(1(0(0(1(2(1(1(0(1(2(0(1(1(x0))))))))))))))))))))))))))))
L(1(0(2(0(0(0(1(0(0(2(1(2(1(2(0(0(1(2(1(2(2(2(0(x0)))))))))))))))))))))))) → D(1(1(0(0(1(2(0(2(1(1(0(1(1(0(0(1(0(2(0(0(1(0(0(1(2(2(0(x0))))))))))))))))))))))))))))
L(1(0(2(1(0(2(1(2(2(2(0(1(0(1(1(1(2(2(0(1(1(1(1(x0)))))))))))))))))))))))) → D(1(0(2(0(1(1(0(1(1(0(2(0(0(1(0(0(2(0(1(1(2(2(1(1(0(0(0(x0))))))))))))))))))))))))))))
L(1(0(2(1(1(2(0(0(0(2(1(2(1(0(0(1(2(0(2(0(1(1(1(x0)))))))))))))))))))))))) → D(1(0(1(1(0(0(1(1(1(0(1(1(1(2(1(0(1(2(2(2(1(1(1(1(1(1(0(x0))))))))))))))))))))))))))))
L(1(1(0(0(2(2(1(2(0(1(1(0(1(2(2(1(1(2(1(0(0(2(1(x0)))))))))))))))))))))))) → D(1(2(2(0(2(1(1(2(1(1(1(1(0(1(1(1(2(1(1(2(1(2(1(1(2(1(0(x0))))))))))))))))))))))))))))
L(1(1(0(1(1(2(0(0(0(2(2(2(1(0(1(2(1(1(0(0(1(0(1(x0)))))))))))))))))))))))) → D(1(1(0(2(0(1(1(0(2(1(0(1(0(0(1(1(1(0(1(0(1(2(1(0(1(2(1(x0))))))))))))))))))))))))))))
L(1(1(1(0(2(1(1(0(0(0(2(1(1(0(2(0(2(2(0(2(0(2(1(x0)))))))))))))))))))))))) → D(1(1(0(1(2(2(0(2(1(2(1(2(2(0(0(0(2(1(1(2(1(0(0(0(1(2(1(x0))))))))))))))))))))))))))))
L(1(1(1(2(1(1(1(1(2(2(1(2(1(2(2(1(2(1(0(0(1(0(2(x0)))))))))))))))))))))))) → D(1(1(0(1(1(0(1(1(2(1(1(1(0(1(0(1(0(1(2(2(0(0(0(1(0(0(0(x0))))))))))))))))))))))))))))
L(1(1(2(1(1(0(1(1(0(1(2(1(1(2(2(2(0(0(0(1(2(0(1(x0)))))))))))))))))))))))) → D(1(1(0(1(0(2(2(2(1(1(0(2(1(1(0(2(1(0(0(1(1(1(1(1(1(1(1(x0))))))))))))))))))))))))))))
L(1(1(2(1(2(2(2(2(1(1(0(0(1(1(2(1(2(1(2(0(0(0(0(x0)))))))))))))))))))))))) → D(1(0(0(2(2(1(1(0(0(0(1(1(2(0(1(0(0(0(1(2(1(1(1(0(0(2(0(x0))))))))))))))))))))))))))))
L(1(2(0(0(2(0(1(2(2(2(1(1(0(1(2(1(1(2(1(1(1(0(0(x0)))))))))))))))))))))))) → D(1(0(1(0(0(0(2(1(2(2(0(0(1(0(0(0(1(2(1(2(2(2(1(1(1(0(0(x0))))))))))))))))))))))))))))
L(1(2(0(1(1(2(1(1(1(2(1(1(2(1(1(0(1(0(0(2(0(2(2(x0)))))))))))))))))))))))) → D(1(0(1(0(1(1(2(1(1(0(2(0(2(1(1(1(1(0(1(2(0(1(0(2(1(0(1(x0))))))))))))))))))))))))))))
L(1(2(0(2(2(1(0(1(0(0(2(0(0(0(1(2(1(2(2(0(1(1(1(x0)))))))))))))))))))))))) → D(1(0(0(2(1(1(0(2(2(0(1(0(2(0(0(1(2(2(2(1(0(0(1(1(0(1(1(x0))))))))))))))))))))))))))))
L(1(2(0(2(2(1(0(1(2(1(1(2(1(1(2(2(0(2(1(2(1(2(0(x0)))))))))))))))))))))))) → D(1(2(2(2(1(1(2(1(0(2(0(0(2(2(2(1(2(1(0(0(2(1(0(0(2(1(1(x0))))))))))))))))))))))))))))
L(1(2(1(0(1(1(2(0(0(2(2(1(2(1(1(2(2(2(1(2(1(0(0(x0)))))))))))))))))))))))) → D(1(2(1(2(2(2(2(0(2(1(1(1(2(1(2(1(1(0(0(1(2(1(1(1(1(2(1(x0))))))))))))))))))))))))))))
L(1(2(1(1(0(1(1(1(2(2(1(2(1(0(1(2(1(2(0(1(2(0(0(x0)))))))))))))))))))))))) → D(1(0(2(1(1(0(0(1(1(1(1(0(0(0(1(0(0(0(2(2(1(0(1(0(0(1(0(x0))))))))))))))))))))))))))))
L(1(2(1(1(2(2(2(1(0(0(2(1(0(2(0(2(1(2(1(1(2(2(0(x0)))))))))))))))))))))))) → D(1(1(1(2(1(0(1(1(1(2(2(2(0(2(1(2(2(2(1(1(0(0(0(0(2(1(0(x0))))))))))))))))))))))))))))
L(1(2(1(2(1(2(2(0(2(0(1(1(0(0(1(0(1(0(2(0(1(1(1(x0)))))))))))))))))))))))) → D(1(0(1(0(2(1(1(1(1(0(1(2(1(0(2(2(0(0(0(0(1(2(0(1(0(2(1(x0))))))))))))))))))))))))))))
L(1(2(2(1(2(1(2(2(0(0(2(1(0(2(0(0(1(2(1(2(0(2(1(x0)))))))))))))))))))))))) → D(1(1(2(0(1(0(1(0(1(0(1(2(0(0(1(2(1(1(1(2(0(0(2(2(2(1(1(x0))))))))))))))))))))))))))))
L(1(2(2(1(2(2(0(2(2(2(2(1(1(1(0(1(1(0(1(1(0(0(0(x0)))))))))))))))))))))))) → D(1(0(2(1(1(1(0(0(1(0(1(2(2(2(2(0(2(0(2(0(0(2(1(2(1(2(1(x0))))))))))))))))))))))))))))
L(2(0(0(2(0(0(0(1(1(2(1(2(1(1(0(1(1(1(0(2(1(2(1(x0)))))))))))))))))))))))) → D(1(2(1(0(1(1(1(0(1(1(1(2(1(0(2(0(1(0(1(0(0(0(2(1(1(0(0(x0))))))))))))))))))))))))))))
L(2(1(0(0(0(2(2(0(1(2(1(0(2(2(2(2(1(2(1(0(1(1(0(x0)))))))))))))))))))))))) → D(0(2(1(2(1(1(2(0(1(2(0(1(2(1(0(0(0(0(2(2(1(0(2(0(1(0(1(x0))))))))))))))))))))))))))))
L(2(1(1(0(0(2(1(1(0(1(2(0(1(0(0(0(0(0(1(1(2(0(2(x0)))))))))))))))))))))))) → D(2(1(1(1(0(0(0(0(2(1(1(0(0(0(1(1(2(1(1(0(0(1(2(0(0(1(2(x0))))))))))))))))))))))))))))
L(2(1(1(0(1(0(2(1(2(2(1(0(1(2(2(1(0(0(2(0(1(1(0(x0)))))))))))))))))))))))) → D(2(1(1(1(1(0(2(1(2(0(2(0(1(1(0(1(2(1(2(0(0(1(2(1(1(1(1(x0))))))))))))))))))))))))))))
L(2(1(1(0(2(1(2(1(2(0(1(2(1(1(0(2(2(1(0(0(1(2(0(x0)))))))))))))))))))))))) → D(0(0(1(0(1(1(1(1(2(0(1(1(0(0(0(0(2(1(1(1(2(2(0(0(1(1(0(x0))))))))))))))))))))))))))))
L(2(1(2(0(1(2(0(1(2(1(1(0(0(0(2(2(1(2(1(0(1(2(0(x0)))))))))))))))))))))))) → D(0(0(0(0(0(1(2(1(0(2(0(1(2(2(2(0(0(0(2(1(0(0(0(1(2(1(1(x0))))))))))))))))))))))))))))
L(2(2(1(0(0(0(0(2(0(0(1(1(1(0(2(1(1(0(0(1(1(1(1(x0)))))))))))))))))))))))) → D(1(0(2(1(2(1(0(0(1(1(0(1(1(0(0(2(0(0(2(1(0(2(1(1(1(2(1(x0))))))))))))))))))))))))))))
L(2(2(2(1(0(2(0(1(1(0(1(0(2(1(0(2(1(2(1(2(1(2(1(x0)))))))))))))))))))))))) → D(1(1(2(1(2(1(0(1(1(1(1(2(2(0(0(0(0(0(1(2(1(0(1(1(0(0(1(x0))))))))))))))))))))))))))))
Y0(D(x0)) → D(0(x0))
Y1(D(x0)) → D(1(x0))
Y2(D(x0)) → D(2(x0))
R(D(x0)) → B(x0)

Proof

1 Termination Assumption

We assume termination of the following TRS
B(x0) → W(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(M(V(x0))))))))))))))))))))))))
M(x0) → x0
M(V(0(x0))) → V(X0(x0))
M(V(1(x0))) → V(X1(x0))
M(V(2(x0))) → V(X2(x0))
X0(0(x0)) → 0(X0(x0))
X0(1(x0)) → 1(X0(x0))
X0(2(x0)) → 2(X0(x0))
X1(0(x0)) → 0(X1(x0))
X1(1(x0)) → 1(X1(x0))
X1(2(x0)) → 2(X1(x0))
X2(0(x0)) → 0(X2(x0))
X2(1(x0)) → 1(X2(x0))
X2(2(x0)) → 2(X2(x0))
X0(E(x0)) → 0(E(x0))
X1(E(x0)) → 1(E(x0))
X2(E(x0)) → 2(E(x0))
W(V(x0)) → R(L(x0))
L(0(x0)) → Y0(L(x0))
L(1(x0)) → Y1(L(x0))
L(2(x0)) → Y2(L(x0))
L(0(0(0(0(0(1(0(1(2(0(1(1(0(0(0(0(2(0(1(2(2(1(0(x0)))))))))))))))))))))))) → D(2(1(2(0(0(2(2(1(0(1(0(0(1(0(0(0(1(0(2(1(1(2(1(2(2(1(0(x0))))))))))))))))))))))))))))
L(0(0(0(2(1(0(2(1(0(1(1(2(1(2(2(0(0(2(2(1(1(1(0(x0)))))))))))))))))))))))) → D(0(1(0(0(1(0(1(1(2(1(1(1(2(0(0(0(2(1(2(0(0(1(2(1(1(0(1(x0))))))))))))))))))))))))))))
L(0(0(0(2(1(1(0(1(0(1(1(2(2(0(0(2(1(0(2(1(1(1(0(x0)))))))))))))))))))))))) → D(1(0(1(1(2(0(2(1(0(0(0(1(1(0(2(1(0(0(1(0(0(0(1(1(2(1(1(x0))))))))))))))))))))))))))))
L(0(0(0(2(2(1(1(0(1(0(0(2(1(2(0(1(2(1(2(1(0(2(2(x0)))))))))))))))))))))))) → D(1(0(0(0(0(1(0(1(1(1(1(1(0(2(1(0(2(1(2(1(1(0(1(1(0(2(1(x0))))))))))))))))))))))))))))
L(0(0(1(1(0(1(0(0(1(0(0(2(0(1(2(2(0(2(0(1(1(0(0(x0)))))))))))))))))))))))) → D(0(1(2(1(1(2(1(2(2(0(0(2(1(0(0(1(0(1(2(0(2(2(1(1(1(1(0(x0))))))))))))))))))))))))))))
L(0(0(1(2(1(2(2(0(0(0(1(0(0(0(0(1(0(1(2(1(2(0(1(x0)))))))))))))))))))))))) → D(1(0(0(2(0(0(2(1(1(1(0(0(0(0(0(1(0(2(1(1(2(2(1(1(0(1(0(x0))))))))))))))))))))))))))))
L(0(0(2(0(2(1(0(0(2(1(0(1(2(2(2(1(0(1(0(2(1(2(1(x0)))))))))))))))))))))))) → D(1(1(0(0(0(0(1(1(2(0(1(0(2(1(2(2(1(0(0(2(1(0(0(2(1(1(1(x0))))))))))))))))))))))))))))
L(0(0(2(1(1(2(1(0(2(2(2(0(0(0(0(2(2(1(0(1(0(0(0(x0)))))))))))))))))))))))) → D(1(0(2(1(0(1(0(2(1(2(1(1(0(0(2(0(1(0(2(2(1(2(0(1(1(1(0(x0))))))))))))))))))))))))))))
L(0(1(0(2(1(0(2(1(0(1(2(1(0(2(2(2(1(0(0(1(1(2(0(x0)))))))))))))))))))))))) → D(1(0(2(1(1(0(1(0(1(0(0(0(2(0(1(0(2(0(1(0(2(1(1(0(1(1(1(x0))))))))))))))))))))))))))))
L(0(1(0(2(2(1(0(1(2(2(1(0(2(1(1(2(1(2(2(1(2(1(1(x0)))))))))))))))))))))))) → D(0(2(1(0(0(1(2(0(2(2(1(0(2(1(1(1(1(0(1(1(0(0(1(0(0(2(0(x0))))))))))))))))))))))))))))
L(0(1(2(0(2(0(2(2(1(1(0(0(2(1(1(2(0(0(0(0(2(1(1(x0)))))))))))))))))))))))) → D(0(0(0(2(1(1(1(2(0(2(2(2(1(1(0(1(2(1(2(1(0(0(2(0(1(0(1(x0))))))))))))))))))))))))))))
L(0(1(2(1(0(1(1(0(2(0(1(1(2(2(2(1(0(2(2(0(0(1(0(x0)))))))))))))))))))))))) → D(2(1(1(0(1(1(0(2(0(1(2(1(0(1(1(2(2(1(2(2(1(0(0(1(2(0(1(x0))))))))))))))))))))))))))))
L(0(1(2(1(2(1(0(0(1(0(2(0(2(1(1(2(1(1(0(2(1(1(0(x0)))))))))))))))))))))))) → D(0(1(1(1(1(1(1(1(0(1(1(1(2(1(1(0(2(1(2(1(2(1(1(0(0(1(1(x0))))))))))))))))))))))))))))
L(0(1(2(2(2(1(1(2(2(2(2(2(1(0(1(1(1(1(2(1(0(1(1(x0)))))))))))))))))))))))) → D(2(1(2(0(0(1(2(2(1(1(2(0(1(1(0(0(2(2(0(2(1(1(1(0(0(1(1(x0))))))))))))))))))))))))))))
L(0(2(1(0(0(2(0(0(1(1(1(0(1(1(2(1(1(0(1(1(2(1(1(x0)))))))))))))))))))))))) → D(2(1(0(0(1(0(2(1(1(1(1(1(1(1(1(0(2(1(1(0(1(0(0(0(1(2(1(x0))))))))))))))))))))))))))))
L(0(2(2(0(2(1(0(2(0(2(2(1(0(1(0(1(0(0(2(1(0(0(0(x0)))))))))))))))))))))))) → D(0(1(1(2(1(0(1(0(1(1(0(0(1(2(1(1(2(2(1(2(0(1(0(0(1(2(0(x0))))))))))))))))))))))))))))
L(0(2(2(1(0(1(1(0(1(0(2(1(1(0(0(0(0(2(1(0(2(2(2(x0)))))))))))))))))))))))) → D(0(0(0(1(2(1(2(1(1(2(2(2(1(1(0(1(0(2(1(1(0(0(1(2(1(1(0(x0))))))))))))))))))))))))))))
L(1(0(0(0(0(0(0(1(2(1(1(0(2(0(1(2(2(2(2(1(1(0(0(x0)))))))))))))))))))))))) → D(1(2(0(0(2(1(2(1(0(1(1(2(1(0(1(2(1(0(2(1(1(2(1(2(2(2(1(x0))))))))))))))))))))))))))))
L(1(0(0(2(1(1(0(2(1(1(2(0(0(0(2(0(0(0(1(1(1(2(0(x0)))))))))))))))))))))))) → D(1(0(1(0(1(0(2(1(1(1(2(1(0(0(1(0(2(1(0(1(0(2(1(2(2(2(0(x0))))))))))))))))))))))))))))
L(1(0(1(2(0(0(0(2(1(0(0(1(0(0(1(2(2(1(0(2(0(0(0(x0)))))))))))))))))))))))) → D(1(0(0(1(0(2(1(2(2(0(1(0(0(1(1(0(0(1(2(1(1(0(1(2(0(1(1(x0))))))))))))))))))))))))))))
L(1(0(2(0(0(0(1(0(0(2(1(2(1(2(0(0(1(2(1(2(2(2(0(x0)))))))))))))))))))))))) → D(1(1(0(0(1(2(0(2(1(1(0(1(1(0(0(1(0(2(0(0(1(0(0(1(2(2(0(x0))))))))))))))))))))))))))))
L(1(0(2(1(0(2(1(2(2(2(0(1(0(1(1(1(2(2(0(1(1(1(1(x0)))))))))))))))))))))))) → D(1(0(2(0(1(1(0(1(1(0(2(0(0(1(0(0(2(0(1(1(2(2(1(1(0(0(0(x0))))))))))))))))))))))))))))
L(1(0(2(1(1(2(0(0(0(2(1(2(1(0(0(1(2(0(2(0(1(1(1(x0)))))))))))))))))))))))) → D(1(0(1(1(0(0(1(1(1(0(1(1(1(2(1(0(1(2(2(2(1(1(1(1(1(1(0(x0))))))))))))))))))))))))))))
L(1(1(0(0(2(2(1(2(0(1(1(0(1(2(2(1(1(2(1(0(0(2(1(x0)))))))))))))))))))))))) → D(1(2(2(0(2(1(1(2(1(1(1(1(0(1(1(1(2(1(1(2(1(2(1(1(2(1(0(x0))))))))))))))))))))))))))))
L(1(1(0(1(1(2(0(0(0(2(2(2(1(0(1(2(1(1(0(0(1(0(1(x0)))))))))))))))))))))))) → D(1(1(0(2(0(1(1(0(2(1(0(1(0(0(1(1(1(0(1(0(1(2(1(0(1(2(1(x0))))))))))))))))))))))))))))
L(1(1(1(0(2(1(1(0(0(0(2(1(1(0(2(0(2(2(0(2(0(2(1(x0)))))))))))))))))))))))) → D(1(1(0(1(2(2(0(2(1(2(1(2(2(0(0(0(2(1(1(2(1(0(0(0(1(2(1(x0))))))))))))))))))))))))))))
L(1(1(1(2(1(1(1(1(2(2(1(2(1(2(2(1(2(1(0(0(1(0(2(x0)))))))))))))))))))))))) → D(1(1(0(1(1(0(1(1(2(1(1(1(0(1(0(1(0(1(2(2(0(0(0(1(0(0(0(x0))))))))))))))))))))))))))))
L(1(1(2(1(1(0(1(1(0(1(2(1(1(2(2(2(0(0(0(1(2(0(1(x0)))))))))))))))))))))))) → D(1(1(0(1(0(2(2(2(1(1(0(2(1(1(0(2(1(0(0(1(1(1(1(1(1(1(1(x0))))))))))))))))))))))))))))
L(1(1(2(1(2(2(2(2(1(1(0(0(1(1(2(1(2(1(2(0(0(0(0(x0)))))))))))))))))))))))) → D(1(0(0(2(2(1(1(0(0(0(1(1(2(0(1(0(0(0(1(2(1(1(1(0(0(2(0(x0))))))))))))))))))))))))))))
L(1(2(0(0(2(0(1(2(2(2(1(1(0(1(2(1(1(2(1(1(1(0(0(x0)))))))))))))))))))))))) → D(1(0(1(0(0(0(2(1(2(2(0(0(1(0(0(0(1(2(1(2(2(2(1(1(1(0(0(x0))))))))))))))))))))))))))))
L(1(2(0(1(1(2(1(1(1(2(1(1(2(1(1(0(1(0(0(2(0(2(2(x0)))))))))))))))))))))))) → D(1(0(1(0(1(1(2(1(1(0(2(0(2(1(1(1(1(0(1(2(0(1(0(2(1(0(1(x0))))))))))))))))))))))))))))
L(1(2(0(2(2(1(0(1(0(0(2(0(0(0(1(2(1(2(2(0(1(1(1(x0)))))))))))))))))))))))) → D(1(0(0(2(1(1(0(2(2(0(1(0(2(0(0(1(2(2(2(1(0(0(1(1(0(1(1(x0))))))))))))))))))))))))))))
L(1(2(0(2(2(1(0(1(2(1(1(2(1(1(2(2(0(2(1(2(1(2(0(x0)))))))))))))))))))))))) → D(1(2(2(2(1(1(2(1(0(2(0(0(2(2(2(1(2(1(0(0(2(1(0(0(2(1(1(x0))))))))))))))))))))))))))))
L(1(2(1(0(1(1(2(0(0(2(2(1(2(1(1(2(2(2(1(2(1(0(0(x0)))))))))))))))))))))))) → D(1(2(1(2(2(2(2(0(2(1(1(1(2(1(2(1(1(0(0(1(2(1(1(1(1(2(1(x0))))))))))))))))))))))))))))
L(1(2(1(1(0(1(1(1(2(2(1(2(1(0(1(2(1(2(0(1(2(0(0(x0)))))))))))))))))))))))) → D(1(0(2(1(1(0(0(1(1(1(1(0(0(0(1(0(0(0(2(2(1(0(1(0(0(1(0(x0))))))))))))))))))))))))))))
L(1(2(1(1(2(2(2(1(0(0(2(1(0(2(0(2(1(2(1(1(2(2(0(x0)))))))))))))))))))))))) → D(1(1(1(2(1(0(1(1(1(2(2(2(0(2(1(2(2(2(1(1(0(0(0(0(2(1(0(x0))))))))))))))))))))))))))))
L(1(2(1(2(1(2(2(0(2(0(1(1(0(0(1(0(1(0(2(0(1(1(1(x0)))))))))))))))))))))))) → D(1(0(1(0(2(1(1(1(1(0(1(2(1(0(2(2(0(0(0(0(1(2(0(1(0(2(1(x0))))))))))))))))))))))))))))
L(1(2(2(1(2(1(2(2(0(0(2(1(0(2(0(0(1(2(1(2(0(2(1(x0)))))))))))))))))))))))) → D(1(1(2(0(1(0(1(0(1(0(1(2(0(0(1(2(1(1(1(2(0(0(2(2(2(1(1(x0))))))))))))))))))))))))))))
L(1(2(2(1(2(2(0(2(2(2(2(1(1(1(0(1(1(0(1(1(0(0(0(x0)))))))))))))))))))))))) → D(1(0(2(1(1(1(0(0(1(0(1(2(2(2(2(0(2(0(2(0(0(2(1(2(1(2(1(x0))))))))))))))))))))))))))))
L(2(0(0(2(0(0(0(1(1(2(1(2(1(1(0(1(1(1(0(2(1(2(1(x0)))))))))))))))))))))))) → D(1(2(1(0(1(1(1(0(1(1(1(2(1(0(2(0(1(0(1(0(0(0(2(1(1(0(0(x0))))))))))))))))))))))))))))
L(2(1(0(0(0(2(2(0(1(2(1(0(2(2(2(2(1(2(1(0(1(1(0(x0)))))))))))))))))))))))) → D(0(2(1(2(1(1(2(0(1(2(0(1(2(1(0(0(0(0(2(2(1(0(2(0(1(0(1(x0))))))))))))))))))))))))))))
L(2(1(1(0(0(2(1(1(0(1(2(0(1(0(0(0(0(0(1(1(2(0(2(x0)))))))))))))))))))))))) → D(2(1(1(1(0(0(0(0(2(1(1(0(0(0(1(1(2(1(1(0(0(1(2(0(0(1(2(x0))))))))))))))))))))))))))))
L(2(1(1(0(1(0(2(1(2(2(1(0(1(2(2(1(0(0(2(0(1(1(0(x0)))))))))))))))))))))))) → D(2(1(1(1(1(0(2(1(2(0(2(0(1(1(0(1(2(1(2(0(0(1(2(1(1(1(1(x0))))))))))))))))))))))))))))
L(2(1(1(0(2(1(2(1(2(0(1(2(1(1(0(2(2(1(0(0(1(2(0(x0)))))))))))))))))))))))) → D(0(0(1(0(1(1(1(1(2(0(1(1(0(0(0(0(2(1(1(1(2(2(0(0(1(1(0(x0))))))))))))))))))))))))))))
L(2(1(2(0(1(2(0(1(2(1(1(0(0(0(2(2(1(2(1(0(1(2(0(x0)))))))))))))))))))))))) → D(0(0(0(0(0(1(2(1(0(2(0(1(2(2(2(0(0(0(2(1(0(0(0(1(2(1(1(x0))))))))))))))))))))))))))))
L(2(2(1(0(0(0(0(2(0(0(1(1(1(0(2(1(1(0(0(1(1(1(1(x0)))))))))))))))))))))))) → D(1(0(2(1(2(1(0(0(1(1(0(1(1(0(0(2(0(0(2(1(0(2(1(1(1(2(1(x0))))))))))))))))))))))))))))
L(2(2(2(1(0(2(0(1(1(0(1(0(2(1(0(2(1(2(1(2(1(2(1(x0)))))))))))))))))))))))) → D(1(1(2(1(2(1(0(1(1(1(1(2(2(0(0(0(0(0(1(2(1(0(1(1(0(0(1(x0))))))))))))))))))))))))))))
Y0(D(x0)) → D(0(x0))
Y1(D(x0)) → D(1(x0))
Y2(D(x0)) → D(2(x0))
R(D(x0)) → B(x0)